Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1’s function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.     

Dynamics of orientation selectivity in the primary visual cortex and the importance of cortical inhibition

To test theories of orientation selectivity in primary visual cortex (V1), we have done experiments to measure the dynamics of orientation tuning of single neurons in the V1 cortex of macaque monkeys. Based on our dynamics results, we propose that a V1 cell's orientation selectivity is generated mainly by both tuned enhancement and global suppression. Enhancement near the preferred orientation is probably caused by feed-forward input from LGN (plus amplification by cortical-cortical interaction). Global suppression could be supplied by cortical inhibition. Additionally, in about 1/3 of V1 neurons (usually the most sharply tuned) there is tuned suppression, centered near the cell's preferred orientation but broader than tuned enhancement. These mechanisms also can explain important features of steady-state selectivity in the V1 neuron population. Furthermore, similar neuronal mechanisms may be used generally throughout the cerebral cortex.     

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

Feedforward origins of response variability underlying contrast invariant orientation tuning in cat visual cortex

Contrast invariant orientation tuning in simple cells of the visual cortex depends critically on contrast dependent trial-to-trial variability in their membrane potential responses. This observation raises the question of whether this variability originates from within the cortical circuit or the feedforward inputs from the lateral geniculate nucleus (LGN). To distinguish between these two sources of variability, we first measured membrane potential responses while inactivating the surrounding cortex, and found that response variability was nearly unaffected. We then studied variability in the LGN, including contrast dependence, and the trial-to-trial correlation in responses between nearby neurons. Variability decreased significantly with contrast, whereas correlation changed little. When these experimentally measured parameters of variability were applied to a feedforward model of simple cells that included realistic mechanisms of synaptic integration, contrast-dependent, orientation independent variability emerged in the membrane potential responses. Analogous mechanisms might contribute to the stimulus dependence and propagation of variability throughout the neocortex.     

Learning receptive field properties of complex cells in V1

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.     

A minimal mechanistic model for temporal signal processing in the lateral geniculate nucleus

The receptive fields of cells in the lateral geniculate nucleus (LGN) are shaped by their diverse set of impinging inputs: feedforward synaptic inputs stemming from retina, and feedback inputs stemming from the visual cortex and the thalamic reticular nucleus. To probe the possible roles of these feedforward and feedback inputs in shaping the temporal receptive-field structure of LGN relay cells, we here present and investigate a minimal mechanistic firing-rate model tailored to elucidate their disparate features. The model for LGN relay ON cells includes feedforward excitation and inhibition (via interneurons) from retinal ON cells and excitatory and inhibitory (via thalamic reticular nucleus cells and interneurons) feedback from cortical ON and OFF cells. From a general firing-rate model formulated in terms of Volterra integral equations, we derive a single delay differential equation with absolute delay governing the dynamics of the system. A freely available and easy-to-use GUI-based MATLAB version of this minimal mechanistic LGN circuit model is provided. We particularly investigate the LGN relay-cell impulse response and find through thorough explorations of the model’s parameter space that both purely feedforward models and feedback models with feedforward excitation only, can account quantitatively for previously reported experimental results. We find, however, that the purely feedforward model predicts two impulse response measures, the time to first peak and the biphasic index (measuring the relative weight of the rebound phase) to be anticorrelated. In contrast, the models with feedback predict different correlations between these two measures. This suggests an experimental test assessing the relative importance of feedforward and feedback connections in shaping the impulse response of LGN relay cells.     

A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.     

Development of spatial coarse-to-fine processing in the visual pathway

The sequential analysis of information in a coarse-to-fine manner is a fundamental mode of processing in the visual pathway. Spatial frequency (SF) tuning, arguably the most fundamental feature of spatial vision, provides particular intuition within the coarse-to-fine framework: low spatial frequencies convey global information about an image (e.g., general orientation), while high spatial frequencies carry more detailed information (e.g., edges). In this paper, we study the development of cortical spatial frequency tuning. As feedforward input from the lateral geniculate nucleus (LGN) has been shown to have significant influence on cortical coarse-to-fine processing, we present a firing-rate based thalamocortical model which includes both feedforward and feedback components. We analyze the relationship between various model parameters (including cortical feedback strength) and responses. We confirm the importance of the antagonistic relationship between the center and surround responses in thalamic relay cell receptive fields (RFs), and further characterize how specific structural LGN RF parameters affect cortical coarse-to-fine processing. Our results also indicate that the effect of cortical feedback on spatial frequency tuning is age-dependent: in particular, cortical feedback more strongly affects coarse-to-fine processing in kittens than in adults. We use our results to propose an experimentally testable hypothesis for the function of the extensive feedback in the corticothalamic circuit.     

Retinal and cortical nonlinearities combine to produce masking in V1 responses to plaids

The visual response of a cell in the primary visual cortex (V1) to a drifting grating stimulus at the cell’s preferred orientation decreases when a second, perpendicular, grating is superimposed. This effect is called masking. To understand the nonlinear masking effect, we model the response of Macaque V1 simple cells in layer 4Cα to input from magnocellular Lateral Geniculate Nucleus (LGN) cells. The cortical model network is a coarse-grained reduction of an integrate-and-fire network with excitation from LGN input and inhibition from other cortical neurons. The input is modeled as a sum of LGN cell responses. Each LGN cell is modeled as the convolution of a spatio-temporal filter with the visual stimulus, normalized by a retinal contrast gain control, and followed by rectification representing the LGN spike threshold. In our model, the experimentally observed masking arises at the level of LGN input to the cortex. The cortical network effectively induces a dynamic threshold that forces the test grating to have high contrast before it can overcome the masking provided by the perpendicular grating. The subcortical nonlinearities and the cortical network together account for the masking effect. Melinda Koelling is formerly from Center for Neural Science and Courant Institute, New York University.     

Determination of the fraction of active inputs required by a neuron to fire

What fraction of the inputs to a neuron in the primary visual cortex (V1) need to be active for that neuron to reach its firing threshold? The paper describes a numerical method for estimating the selectivity of visual neurons, in terms of the required fraction of active excitatory inputs, from standard data produced by intracellular electro-physiological recordings. The method also provides an estimate of the relative strength of the feedforward inhibition in a push-pull model of the inputs to V1 simple cells. The method is tested on two V1 cells described in Carandini and Ferster [Carandini, M., Ferster, D., 2000. Membrane potential and firing rate in cat primary visual cortex. J. Neurosci. 20, 470-484]. The results indicate that the maximum strength of feedforward inhibition is around 30% of the maximum strength of feedforward excitation. The two V1 neurons investigated fire if more than around 40% of their excitatory LGN inputs are active.     

S cone contributions to the magnocellular visual pathway in macaque monkey

The magnocellular visual pathway is believed to receive input from long (L) and middle (M), but not short (S), wavelength-sensitive cones. Recording from neurons in magnocellular layers of lateral geniculate nucleus (LGN) in macaque monkeys, we found that magnocellular neurons were unequivocally responsive to S cone-isolating stimuli. A quantitative analysis suggests that S cones provided about 10% of the input to these cells, on average, while L:M ratios were far more variable. S cone signals influenced responses with the same sign as L and M cone inputs (i.e., no color opponency). Magnocellular afferent recordings following inactivation of primary visual cortex demonstrated that S cone signals were feedforward in nature and did not arise from cortical feedback to LGN     

Visual Receptive Field Properties of Neurons in the Mouse Lateral Geniculate Nucleus

The lateral geniculate nucleus (LGN) is increasingly regarded as a “smart-gating” operator for processing visual information. Therefore, characterizing the response properties of LGN neurons will enable us to better understand how neurons encode and transfer visual signals. Efforts have been devoted to study its anatomical and functional features, and recent advances have highlighted the existence in rodents of complex features such as direction/orientation selectivity. However, unlike well-researched higher-order mammals such as primates, the full array of response characteristics vis-à-vis its morphological features have remained relatively unexplored in the mouse LGN. To address the issue, we recorded from mouse LGN neurons using multisite-electrode-arrays (MEAs) and analysed their discharge patterns in relation to their location under a series of visual stimulation paradigms. Several response properties paralleled results from earlier studies in the field and these include centre-surround organization, size of receptive field, spontaneous firing rate and linearity of spatial summation. However, our results also revealed “high-pass” and “low-pass” features in the temporal frequency tuning of some cells, and greater average contrast gain than reported by earlier studies. In addition, a small proportion of cells had direction/orientation selectivity. Both “high-pass” and “low-pass” cells, as well as direction and orientation selective cells, were found only in small numbers, supporting the notion that these properties emerge in the cortex. ON- and OFF-cells showed distinct contrast sensitivity and temporal frequency tuning properties, suggesting parallel projections from the retina. Incorporating a novel histological technique, we created a 3-D LGN volume model explicitly capturing the morphological features of mouse LGN and localising individual cells into anterior/middle/posterior LGN. Based on this categorization, we show that the ON/OFF, DS/OS and linear response properties are not regionally restricted. Our study confirms earlier findings of spatial pattern selectivity in the LGN, and builds on it to demonstrate that relatively elaborate features are computed early in the visual pathway.     

Predictive Feedback Can Account for Biphasic Responses in the Lateral Geniculate Nucleus

Biphasic neural response properties, where the optimal stimulus for driving a neural response changes from one stimulus pattern to the opposite stimulus pattern over short periods of time, have been described in several visual areas, including lateral geniculate nucleus (LGN), primary visual cortex (V1), and middle temporal area (MT). We describe a hierarchical model of predictive coding and simulations that capture these temporal variations in neuronal response properties. We focus on the LGN-V1 circuit and find that after training on natural images the model exhibits the brain's LGN-V1 connectivity structure, in which the structure of V1 receptive fields is linked to the spatial alignment and properties of center-surround cells in the LGN. In addition, the spatio-temporal response profile of LGN model neurons is biphasic in structure, resembling the biphasic response structure of neurons in cat LGN. Moreover, the model displays a specific pattern of influence of feedback, where LGN receptive fields that are aligned over a simple cell receptive field zone of the same polarity decrease their responses while neurons of opposite polarity increase their responses with feedback. This phase-reversed pattern of influence was recently observed in neurophysiology. These results corroborate the idea that predictive feedback is a general coding strategy in the brain.     

Running as fast as it can: How spiking dynamics form object groupings in the laminar circuits of visual cortex

How spiking neurons cooperate to control behavioral processes is a fundamental problem in computational neuroscience. Such cooperative dynamics are required during visual perception when spatially distributed image fragments are grouped into emergent boundary contours. Perceptual grouping is a challenge for spiking cells because its properties of collinear facilitation and analog sensitivity occur in response to binary spikes with irregular timing across many interacting cells. Some models have demonstrated spiking dynamics in recurrent laminar neocortical circuits, but not how perceptual grouping occurs. Other models have analyzed the fast speed of certain percepts in terms of a single feedforward sweep of activity, but cannot explain other percepts, such as illusory contours, wherein perceptual ambiguity can take hundreds of milliseconds to resolve by integrating multiple spikes over time. The current model reconciles fast feedforward with slower feedback processing, and binary spikes with analog network-level properties, in a laminar cortical network of spiking cells whose emergent properties quantitatively simulate parametric data from neurophysiological experiments, including the formation of illusory contours; the structure of non-classical visual receptive fields; and self-synchronizing gamma oscillations. These laminar dynamics shed new light on how the brain resolves local informational ambiguities through the use of properly designed nonlinear feedback spiking networks which run as fast as they can, given the amount of uncertainty in the data that they process.     

Power-law input-output transfer functions explain the contrast-response and tuning properties of neurons in visual cortex

We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.     

Learning receptive fields using predictive feedback.

Previously, it was suggested that feedback connections from higher- to lower-level areas carry predictions of lower-level neural activities, whereas feedforward connections carry the residual error between the predictions and the actual lower-level activities [Rao, R.P.N., Ballard, D.H., 1999. Nature Neuroscience 2, 79-87.]. A computational model implementing the hypothesis learned simple cell receptive fields when exposed to natural images. Here, we use predictive feedback to explain tuning properties in medial superior temporal area (MST). We implement the hypothesis using a new, biologically plausible, algorithm based on matching pursuit, which retains all the features of the previous implementation, including its ability to efficiently encode input. When presented with natural images, the model developed receptive field properties as found in primary visual cortex. In addition, when exposed to visual motion input resulting from movements through space, the model learned receptive field properties resembling those in MST. These results corroborate the idea that predictive feedback is a general principle used by the visual system to efficiently encode natural input.     

Origin and dynamics of extraclassical suppression in the lateral geniculate nucleus of the macaque monkey

In addition to the classical, center/surround receptive field of neurons in the lateral geniculate nucleus (LGN), there is an extraclassical, nonlinear surround that can strongly suppress LGN responses. This form of suppression likely plays an important role in adjusting the gain of LGN responses to visual stimuli. We performed experiments in alert and anesthetized macaque monkies to quantify extraclassical suppression in the LGN and determine the roles of feedforward and feedback pathways in the generation of LGN suppression. Results show that suppression is significantly stronger among magnocellular neurons than parvocellular neurons and that suppression arises too quickly for involvement from cortical feedback. Furthermore, the amount of suppression supplied by the retina is not significantly different from that in the LGN. These results indicate that extraclassical suppression in the macaque LGN relies on feedforward mechanisms and suggest that suppression in the cortex likely includes a component established in the retina.     

A multi-stage model for fundamental functional properties in primary visual cortex

Many neurons in mammalian primary visual cortex have properties such as sharp tuning for contour orientation, strong selectivity for motion direction, and insensitivity to stimulus polarity, that are not shared with their sub-cortical counterparts. Successful models have been developed for a number of these properties but in one case, direction selectivity, there is no consensus about underlying mechanisms. We here define a model that accounts for many of the empirical observations concerning direction selectivity. The model describes a single column of cat primary visual cortex and comprises a series of processing stages. Each neuron in the first cortical stage receives input from a small number of on-centre and off-centre relay cells in the lateral geniculate nucleus. Consistent with recent physiological evidence, the off-centre inputs to cortex precede the on-centre inputs by a small (～4 ms) interval, and it is this difference that confers direction selectivity on model neurons. We show that the resulting model successfully matches the following empirical data: the proportion of cells that are direction selective; tilted spatiotemporal receptive fields; phase advance in the response to a stationary contrast-reversing grating stepped across the receptive field. The model also accounts for several other fundamental properties. Receptive fields have elongated subregions, orientation selectivity is strong, and the distribution of orientation tuning bandwidth across neurons is similar to that seen in the laboratory. Finally, neurons in the first stage have properties corresponding to simple cells, and more complex-like cells emerge in later stages. The results therefore show that a simple feed-forward model can account for a number of the fundamental properties of primary visual cortex.     

Attention to stimulus features shifts spectral tuning of V4 neurons during natural vision

Previous neurophysiological studies suggest that attention can alter the baseline or gain of neurons in extrastriate visual areas but that it cannot change tuning. This suggests that neurons in visual cortex function as labeled lines whose meaning does not depend on task demands. To test this common assumption, we used a system identification approach to measure spatial frequency and orientation tuning in area V4 during two attentionally demanding visual search tasks, one that required fixation and one that allowed free viewing during search. We found that spatial attention modulates response baseline and gain but does not alter tuning, consistent with previous reports. In contrast, feature-based attention often shifts neuronal tuning. These tuning shifts are inconsistent with the labeled-line model and tend to enhance responses to stimulus features that distinguish the search target. Our data suggest that V4 neurons behave as matched filters that are dynamically tuned to optimize visual search.     

Separation of Spatio-Temporal Receptive Fields into Sums of Gaussian Components

Visual cortical simple cells have been experimentally shown to reveal non-trivial spatio-temporal orientation tuning functions comprising different phases of specifically tuned enhanced and suppressed activity. A recently developed analytical method based on nonlinear neural field models suggests that such space-time responses should be approximately separable into a sum of temporally amplitude modulated Gaussian spatial components. In the present work, we investigate this possibility by means of numerical fits of sums of Gaussians to response functions observed in experiments and computer simulations. Because the theory relates each single component to a particular connectivity kernel between the underlying cell classes shaping the response, the relative contribution of feedforward and cortex-intrinsical excitatory and inhibitory feedback mechanisms to single cell tuning can be approached and quantified in experimental data.